Problem: N different natural numbers are given. If you select four different ones and set them as $ A $, $ B $, $ C $, $ D $, the following formula

$ \ Frac {A + B} {C --D} $



I want to find the maximum value of.




Given N different natural numbers, choose 4 different from them and create a program to find the maximum value of the above formula.



Input

The input is given in the following format.


N
a1 a2 ... aN


The number N (4 ≤ N ≤ 1000) of natural numbers is given in the first line. The value ai (1 ≤ ai ≤ 108) of each natural number is given in the second line. However, the same natural number does not appear more than once (ai ≠ aj for i ≠ j).

Output

Outputs the maximum value of the above formula as a real number for a given N natural numbers. However, the error must not exceed plus or minus 10-5.

Examples

Input

10
1 2 3 4 5 6 7 8 9 10


Output

19.00000


Input

5
22 100 42 3 86


Output

9.78947


Input

6
15 21 36 10 34 5


Output

18.00000


Input

4
100000 99999 8 1


Output

28571.285714

Solution (in CPP):

Solution:
#include "bits/stdc++.h"

using namespace std;

int main (){
	int cnt;
	double max = 0;
	cin >> cnt;
	double s[1000];

	for(int i = 1;i <= cnt;i++){
	cin >> s[i - 1];
	}
	sort(s,s+cnt);
	reverse(s,s+cnt);
	
	for(int n = 0;n <=(cnt - 1);n++){
		for(int l = (n + 1);l <= (cnt - 1);l++){
			int maxone = 0;
			int maxtwo = 1;
			for(int m = 0;m <= 4;m++){
				if(maxone == n)maxone++;
				if(maxtwo == l)maxtwo++;
				if(maxone == l)maxone++;
				if(maxtwo == n)maxtwo++;
				if(maxone == maxtwo)maxtwo++;
			}
			if(n != l){
			double ma = ((s[maxone] + s[maxtwo])/(s[n] - s[l]));
			if(ma > max) max = ma;
			}
		}
	}

	cout << fixed << setprecision(5) <<max <<endl;

	return 0;
}